Question

Find the linear function f(x) for which both f(−2) = 6 and f(0) = −4. Which one of the following matches the correct function?a. f(x) = -1/5xb. f(x) = 6x-4 c. f(x) = -1/5x-4d. -5x-4

Answer 1

Given:

f(x)= ?

f(-2) = 6

f(0) = -4

We will answer this question by testing the options with our given values

`\begin{gathered} A)\text{ f(x)=}(-1)/(5x) \\ f(-2)=\text{ }(-1)/(5(-2)) \\ f(-2)=\text{ }(-1)/(-10) \\ f(-2)=\text{ }(1)/(10) \\ \text{Does not equate with f(-2)=6} \end{gathered}`
`\begin{gathered} B)\text{ f(x)= 6x-4} \\ f(-2)\text{ = 6(-2)-4} \\ f(-2)=-12-4 \\ f(-2)=-16 \\ \text{Does not equate with f(-2)=6} \end{gathered}`
`\begin{gathered} C)\text{ f(x)=}(-1)/(5x-4) \\ f(-2)=\text{ }(-1)/(5(-2)-4) \\ f(-2)=\text{ }(-1)/(-10-4) \\ f(-2)=\text{ }(-1)/(-14) \\ f(-2)=\text{ }(1)/(14) \\ \text{Does not equate with f(-2)=6} \end{gathered}`
`\begin{gathered} f(x)=-5x-4 \\ f(-2)\text{ = -5(-2)-4} \\ f(-2)\text{ = 10-4} \\ f(-2)\text{ = }6. \\ \text{Checks well with original statement} \\ On\text{ the other hand} \\ f(0)\text{ = -5(0) -4} \\ f(0)\text{ = 0-4} \\ f(0)\text{ = -4} \\ \text{Fits well with original statement} \end{gathered}`

Final answer. The right function is f(x)= -5x-4. Option D